论文标题
部分可观测时空混沌系统的无模型预测
Topological Singularity Detection at Multiple Scales
论文作者
论文摘要
假设数据位于现代机器学习研究的主食。然而，最近的工作表明，现实世界数据表现出不同的非字母结构，即奇异性，这可能会导致错误的发现。因此，检测这种奇异性是插值和推理任务的前身至关重要的。我们通过开发一个拓扑框架来解决这个问题，该拓扑框架（i）量化局部固有维度，（ii）产生欧几合性评分，以评估沿多个尺度的点的“多种多样”。我们的方法确定了复杂空间的奇点，同时还捕获了图像数据中的奇异结构和局部几何复杂性。
The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct non-manifold structures, i.e. singularities, that can lead to erroneous findings. Detecting such singularities is therefore crucial as a precursor to interpolation and inference tasks. We address this issue by developing a topological framework that (i) quantifies the local intrinsic dimension, and (ii) yields a Euclidicity score for assessing the 'manifoldness' of a point along multiple scales. Our approach identifies singularities of complex spaces, while also capturing singular structures and local geometric complexity in image data.
